"I can just imagine how disappointed he must be," coach Louis van Gaal told Dutch media after Strootman was injured in AS Roma's 1-0 defeat at Napoli in Serie A on Sunday. "Kevin was in good form.
"For the national side it is a huge blow. Kevin made a huge contribution to our qualification for the World Cup, he never let us down and now his dreams have died."
Strootman will be sidelined for at least six months, according to Dutch media. He tried to play on after sustaining the injury but was eventually carried off on a stretcher.
The midfielder was also taken off before halftime in Wednesday's 2-0 friendly international defeat by France in Paris after hurting his right knee.
Last year Van Gaal said Strootman, captain Robin van Persie and winger Arjen Robben were three players guaranteed a place in his World Cup squad.
The Dutch have been drawn in Group B with champions Spain, Australia and Chile at the finals.